The clip, which is circulating on WhatsApp, shows several men carrying the cardboard model of the tower, which claimed 72 lives when it caught fire in June a year ago, and placing it on a bonfire.
Bobbi Connell, 19, his dad Clifford Smith, 49, and Paul Bussetti, 46, handed themselves into police last night after footage of the horrific joke emerged on social media.
The video, which went viral online, shows a group of people mocking the Grenfell Tower victims as an effigy of the low-income housing bloc, where many migrants lived, goes up in flames in a bonfire.
In June 2017 a total of 72 people perished in the blaze that engulfed the West London tower block - hundreds had their lives utterly devastated with the youngest person to die because of the incident being a stillborn baby.
Officers investigating a model of the Grenfell Tower which was burned on a bonfire have searched the garden of a London property. One man appears to mockingly say, "stay in your flat" as he re-positions the effigy above burning hot coals.
Several onlookers can be heard shouting "help me, help me" and making siren sounds.
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Metropolitan Police Commander Stuart Cundy, who is leading the investigation into the Grenfell Tower tragedy, said he was "frankly appalled by the callous nature" of the video.
'To mock that disaster in such a crude way is vile'.
The video ends as the model is completely consumed by the fire, with one bystander saying: "Perfect".
MEND, an anti-Islamophobia organization, said the "sickening Islamophobic" video amounted to a hate crime.
Communities Secretary James Brokenshire said: "At a time when the bereaved and survivors are giving testimony to the Grenfell inquiry and reliving the unimaginable horror of that tragedy, it beggars belief that anyone should do this".
A spokesperson for the campaign group Justice4Grenfell said the video had "caused great alarm and distress", and added: "We are disgusted and shocked at the inhumanity and callousness of those involved in this video".
Meanwhile, the Prime Minister, fire chiefs and victims have condemned the partygoers. We hope that the police are taking this seriously.